Schaum's Outline of Discrete Mathematics, Revised Third by Seymour Lipschutz

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B) Draw the arrow diagram of R. (c) Find the inverse relation R −1 of R. (d) Determine the domain and range of R. (a) See Fig. 2-6(a) Observe that the rows of the matrix are labeled by the elements of A and the columns by the elements of B. Also observe that the entry in the matrix corresponding to a ∈ A and b ∈ B is 1 if a is related to b and 0 otherwise. (b) See Fig. , iff (a, b) ∈ R. CHAP. 2] RELATIONS 35 Fig. 2-6 (c) Reverse the ordered pairs of R to obtain R −1 : R −1 = {(y, 1), (z, 1), (y, 3), (x, 4), (z, 4)} Observe that by reversing the arrows in Fig.

Two ordered pairs are equal if and only if the corresponding components are equal. Hence we obtain the equations 2x = 6 and x+y =2 from which we derive the answers x = 3 and y = −1. 3. Find the number of relations from A = {a, b, c} to B = {1, 2}. There are 3(2) = 6 elements in A × B, and hence there are m = 26 = 64 subsets of A × B. Thus there are m = 64 relations from A to B. 4. Given A = {1, 2, 3, 4} and B = {x, y, z}. Let R be the following relation from A to B: R = {(1, y), (1, z), (3, y), (4, x), (4, z)} (a) Determine the matrix of the relation.